UNIQUE SOLVABILITY OF UNDER-DETERMINED SPARSE BLIND SEPARATION OF NONNEGATIVE AND OVERLAPPED DATA

摘要

We study the unique solvability of sparse blind separationrnof n non- negative sources from m linear mixtures in thernunder-determined regimem < n. Such source signals arisernin nuclear magnetic resonance data. The geometric propertiesrnof themixturematrix and sparseness structure of sourcernmatrix are closely related to the unique identification of thernmixing matrix. We illustrate and establish necessary andrnsufficient conditions for the unique separation up to scalingrnand permutation. We also present a novel algorithm basedrnon data geometry, source sparseness, and l1 minimization.rnNumerical results substantiate the uniqueness of the sourcernsignal recovery, and show satisfactory performance of ourrnalgorithm on chemical data.